Introducing Weingarten cyclic surfaces in R3
نویسندگان
چکیده
منابع مشابه
On linear Weingarten surfaces
In this paper we study surfaces in Euclidean 3-space that satisfy a Weingarten condition of linear type as κ1 = mκ2 + n, where m and n are real numbers and κ1 and κ2 denote the principal curvatures at each point of the surface. We investigate the possible existence of such surfaces parametrized by a uniparametric family of circles. Besides the surfaces of revolution, we prove that not exist mor...
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In this paper we study properties of linear Weingarten immersions and graphs related to non-existence problems and behaviour of its curvatures. The main results are obtained giving a harmonic representation of linear Weingarten surfaces and by proving optimal estimates of the height and curvatures that the immersion must satisfy, characterizing the spherical caps as the only ones achieving thes...
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A surface in hyperbolic space H 3 invariant by a group of parabolic isometries is called a parabolic surface. In this paper we investigate parabolic surfaces of H 3 that satisfy a linear Weingarten relation of the form aκ1 + bκ2 = c or aH + bK = c, where a, b, c ∈ R and, as usual, κi are the principal curvatures, H is the mean curvature and K is de Gaussian curvature. We classify all parabolic ...
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Introduced in 1861 [1], a Weingarten surface in the Euclidean three-dimensional space E3 is a surface M, whose mean curvature H and Gaussian curvature K satisfy a non-trivial relation Φ(H, K) = 0. Such a surface was introduced by Weingarten. The class of Weingarten surfaces is remarkably large, and it consists of intriguing surfaces in the Euclidean space: the constant mean curvature surfaces, ...
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A linear Weingarten surface in Euclidean space R 3 is a surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH + bK = c, where a, b, c ∈ R. Such a surface is said to be hyperbolic when a + 4bc < 0. In this paper we classify all rotational linear Weingarten surfaces of hyperbolic type. As a consequence, we obtain a family of complete hyperbolic linear Weingarte...
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ژورنال
عنوان ژورنال: Journal of the Egyptian Mathematical Society
سال: 2017
ISSN: 1110-256X
DOI: 10.1016/j.joems.2016.06.001